Stochastic epidemic models with a backward bifurcation
Stochastic epidemic models with a backward bifurcation
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DOI：
10.3934/mbe.2006.3.445
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发表时间：
2006-07-01
影响因子：
2.6
通讯作者：
van den Driessche, P.
中科院分区：
文献类型：
--
作者：
Allen, Linda J. S.;van den Driessche, P.
建立了两个新的随机传染病模型：连续时间马尔可夫链模型和随机微分方程模型。它们基于包括接种疫苗在内的确定性模型，适用于百日咳。对于某些参数值，当疫苗不完美时，确定性模型表现出向后分支。因此，在参数空间的子集中存在双稳区域。在此双稳区域内研究了随机传染病模型的动力学性质，并与确定性模型的动力学性质进行了比较。在该区域内，与感染人群相关的概率分布呈双峰分布，在无病平衡点和较大地方病平衡点各有一种分布模式。当种群规模N>；=1000时，确定性模型与随机模型基本一致，但对于较小的种群规模，随机模型表明后向分叉对疾病动力学的影响很小。
Two new stochastic epidemic models, a continuous-time Markov chain model and a stochastic differential equation model, are formulated. These are based on a deterministic model that includes vaccination and is applicable to pertussis. For some parameter values, the deterministic model exhibits a backward bifurcation if the vaccine is imperfect. Thus a region of bistability exists in a subset of parameter space. The dynamics of the stochastic epidemic models are investigated in this region of bistability, and compared with those of the deterministic model. In this region the probability distribution associated with the infective population exhibits bimodality with one mode at the disease free equilibrium and the other at the larger endemic equilibrium. For population sizes N >= 1000, the deterministic and stochastic models agree, but for small population sizes the stochastic models indicate that the backward bifurcation may have little effect on the disease dynamics.